Identifying phase synchronization clusters in spatially extended dynamical systems.

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean-field approach which allows one to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean-field approach is relatively robust even in configurations where the single-cluster assumption is not entirely fulfilled and (b) that the eigenvalue-decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue-decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis, which account for nonlinearities in the data, are expected to provide complementary information which allows one to gain deeper insights into the collective dynamics of spatially extended complex systems.